I am not sure I understand the problem statement correctly, but it seems to me you are assuming that the chains are horizontal. I visualize a different picture with the chains at an angle. If that is correct, then the tension has a horizontal and a vertical component.

If you visualize the right triangle, you are given the facts regarding the vertical component, and the tension is along the hypotenuse. You don't need the angle to calculate the horizontal component. You can use the Pythagorean theorem.